Figure Series – Reasoning Ability (Odisha TET / Competitive Exams)
Objective – Identify the rule that generates the next figure in a short sequence.
Typical format – 4–5 figures in a row, each an image (square/rectangle, circle, triangle, etc.) with variations in size, orientation, filling, number of elements, symmetry, colour, etc.
Answer type – Multiple‑choice (4 options) or single‑choice.
1. Core Strategy
| Step | What to Do | Why It Helps |
|---|---|---|
| 1. Scan for changes in the figures | Look at size, shape, number of sub‑figures, orientation, colour, shading, line thickness, etc. | A change is the key to the rule. |
| 2. Look for symmetry or balance changes | Count the number of symmetrical halves, mirror images, rotational symmetry. | Many series use symmetry as a hidden pattern. |
| 3. Count elements | Count dots, stars, triangles, etc. or count the total area of filled parts. | Numerical patterns (increasing by 1, doubling, etc.) are common. |
| 4. Observe progression of orientation | 90° rotation, flip, shift left/right, etc. | Rotation/flip often indicates a cyclic pattern. |
| 5. Check for colour alternation | Colour of shapes, background, or outline. | Colour may encode a binary or positional pattern. |
| 6. Combine the above | The rule may involve two variables (e.g., size + orientation). | Complex series are rarely single‑parameter. |
| 7. Verify with all options | Cross‑check each plausible rule with all given options. | Eliminates guesswork. |
2. Common Patterns & “Trick” Points
| Pattern | Typical Signal | Example | Trick |
|---|---|---|---|
| Size increment/decrement | One figure larger or smaller than previous | Square → 2×2 → 3×3 | Size may change non‑linearly (e.g., 2→4→2→8). |
| Number of sub‑figures | 1 → 2 → 3 … | One dot → Two dots side‑by‑side | The number can change directionally (increase then decrease). |
| Rotation Cycle | 0°, 90°, 180°, 270° → repeat | Arrow pointing right, down, left, up | May cycle with a lag (e.g., 0°, 0°, 90°, 90°). |
| Mirror / Flip | Left ↔ Right or Top ↔ Bottom | Mirror image alternates | The flipped figure may also change in size. |
| Colour alternation | Red, Blue, Red, Blue | Circle filled with alternating colours | Colour may encode binary (Red = 1, Blue = 0). |
| Symmetry axis change | Horizontal ↔ Vertical | Symmetry axis flips each step | Often combined with rotation. |
| Composite rule | Two independent changes (size + orientation) | Size increases while orientation rotates | Requires both aspects to be checked. |
| Counting the area of filled vs. empty | Filled area ratio changes | One solid square → half‑filled square | The area can be 1/2, 2/3, etc. |
| Pattern in number of lines | 1 line → 2 lines → 3 lines | A shape with increasing number of straight lines | The lines may be nested or overlapping. |
Tricky Points
- Reverse Direction – The series may reverse after a midpoint (e.g., 1, 3, 5, 3, 1).
- Hidden Dual Pattern – One variable changes while the other stays constant, then switches.
- Unusual Units – “Size” might refer to area rather than side‑length.
- Multiple Colours in One Figure – Check if colours are distributed uniformly or unevenly.
- Non‑Euclidean Shapes – Curved boundaries can mask the underlying pattern (e.g., circle → crescent → full circle).
3. Deriving the Rule – Step‑by‑Step Example
Series
Fig‑1 : 1 small black dot
Fig‑2 : 2 small black dots side‑by‑side
Fig‑3 : 3 small black dots in a row
Fig‑4 : 4 small black dots in a row
| Step | Observation | Inference |
|---|---|---|
| 1 | Count dots: 1, 2, 3, 4 | Linear increase by 1 |
| 2 | All dots are black and size constant | No other change |
| 3 | Orientation: all horizontal | No rotation |
| 4 | Rule: number of dots increases by 1 | Next figure should have 5 dots |
| 5 | Check options – pick the one with 5 dots | Correct answer |
Harder Example
Fig‑1 : 2 triangles pointing up, touching at base
Fig‑2 : 3 triangles pointing up, touching at base
Fig‑3 : 3 triangles pointing down, touching at base
Fig‑4 : 2 triangles pointing down, touching at base
| Step | Observation | Inference |
|---|---|---|
| 1 | Count triangles: 2, 3, 3, 2 | Number changes non‑monotonically |
| 2 | Orientation: up, up, down, down | Orientation alternates after 2 steps |
| 3 | Pattern of count and orientation is independent | Two separate cycles: 2→3→3→2 (length 4) and up→down (length 2) |
| 4 | Next figure: follow the count cycle → 3 triangles | Orientation cycle → up (since we just had down) |
| 5 | Check options – look for 3 triangles pointing up | Pick that option |
4. Important “Formulae” (Not Mathematical, but Rules)
| Rule | Symbolic Representation |
|---|---|
| Linear Count | n_i = n_1 + (i-1) |
| Alternating Orientation | θ_i = θ_1 + (i-1)*90° (mod 360°) |
| Mirror Flip | `F_i = F_{i-1} |